Abstract

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.

Special thanks to Eloy Ayón-Beato and Jasel Berra for useful comments and suggestions. E.R. thanks A. P. Balachandran for the encouragement to the paper. E.R. also acknowledges partial support from grant PROMEP, CA-UV-320: Álgebra, Geometría y Gravitación. M.C. acknowledges support from a CONACyT scholarship (México) under the grant Repatriaciones, Convocatoria 2015-cuarta fase. A.M. acknowledges financial support from PROMEP UASLP-PTC-402 and from CONACYT-México under Project No. CB-2014-243433. This work was partially supported by SNI (México).